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The first sentence was something a friend posted and it confused me, so I asked her why she wrote it like that while also posting mine, however I haven't got an answer yet, so I thought I'd ask here. Which one is correct if either and why? Also, how do you use dass, I don't really understand that yet.
Friend: Ich hoffe dass euch ein schönen Tag habt.
Me: Ich hoffe dass euch einen schönen Tag haben.
Oh, you realize that each of you used two clauses?
One main clause (V2 = verb in 2nd position), one subordinate clause (verb at the end):
[Ich hoffe], dass [ihr einen schönen Tag habt].
So to clear up your case confusion, we consider the second clause only: The pronoun ihr is the subject, hence nominative. The verb follows the subject, i.e. 2nd plural = habt.
To expand this a bit: If the second clause would stand alone, it would have to be a main clause and the word order would shift back to:
Ihr habt einen schönen Tag.
The dass connects both sentences and is called "Konjunktion". Explaining the use of dass would be too much here (one question per post only, please), but canoo would be a place to start, if your German is good enough (which I assume from reading your post).
Regarding the use of dass - and it's counterpart with a single 's', das:
It may help you to memorise that, when used in a clause in a sentence, 'das' means 'which' and 'dass' means '(so) that'.
Even back then, learning it in school, the rule we were taught was "if you can replace 'das/dass' with 'damit' then it's the 2-s/scharfes s form".
Therefore in your example, translate it as
I hope (so) that you have a good day.
A counter-example would be:
Das Abenteuer, das nicht enden will.
The adventure which just won't end.
Note that in both cases you would generally put a comma in front of the 'das' or 'dass'.
